Respuesta :
Answer:
A person must get an IQ score of at least 138.885 to qualify.
Step-by-step explanation:
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this problem, we have that:
[tex]\mu = 115, \sigma = 17[/tex]
(a). [7pts] What IQ score must a person get to qualify
Top 8%, so at least the 100-8 = 92th percentile.
Scores of X and higher, in which X is found when Z has a pvalue of 0.92. So X when Z = 1.405.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.405 = \frac{X - 115}{17}[/tex]
[tex]X - 115 = 17*1.405[/tex]
[tex]X = 138.885[/tex]
A person must get an IQ score of at least 138.885 to qualify.
Answer: The person must score an IQ score of 139 to qualify.
Step-by-step explanation:
Since the IQ scores are normally distributed, we would apply the formula for normal distribution which is expressed as
z = (x - µ)/σ
Where
x = scores on the test.
µ = mean score
σ = standard deviation
From the information given,
µ = 115
σ = 17
The probability value for the upper 8% of the population would be (1 - 8/100) = (1 - 0.08) = 0.92
Looking at the normal distribution table, the z score corresponding to the probability value is 1.41
Therefore,
1.41 = (x - 115)/17
Cross multiplying by 17, it becomes
1.41 × 17 = x - 115
23.97 = x - 115
x = 23.97 + 115
x = 139 to the nearest whole number
